cf. (REF ), the constant 2 in the expectation in (REF ) is replaced by 1 in (REF ), since \(\tilde{x}(\xi )\)  does not have the component \(x^2(\xi )=n^{-1}n^I\)  corresponding to the number of infectives. (Again, \(\alpha ^{(n)}_R\)  and \(\alpha ^{(n)}_{RWR}\)  are no longer relevant.)
The proof of Theorem REF  is easily modified to show that the events \(\tilde{\Omega }_1\)  and
\(\tilde{\Omega }_2\) , with \(A_n\)  replaced by \(\tilde{A}_n=C_1n^{-1}\log n\)  for suitable \(C_1 >0\) , each occur with high probability. It then follows using [1]}, Theorem 4.3 (adapted to \(L^2\)  estimates) that
\({\rm P}\left(\left|\tilde{X}^{(n)}(\tilde{\zeta }^{(n)})-\tilde{x}(\tilde{\zeta })\right|>(1+\tilde{C})\epsilon ^{\prime }\right) \le \frac{4 \tilde{A}_n}{(\delta ^{\prime })^2}+{\rm P}(\tilde{\Omega }_0^c\cup \tilde{\Omega }_1^c \cup \tilde{\Omega }_2^c).\) 
